In my family we'll lose around one or two glass ornaments per year due to the kids using the ornament box in decidedly non-fragile ways. Most people throw away the glass shards from ornaments but if the broken ornament has sentimental value or the bits are pretty you can always break it down into glitter and use that broken-glass-glitter to fill the inside of a transparent ornament.

Household project weblog Grathio Labs shows how you can safely reduce your broken ornament to glass glitter by adding the broken pieces to a freezer bag, double-bagging that bag in another freezer bag, and smashing the bags with a hammer until your glitter reaches the desired consistency. Fill the inside of a transparent glass ball ornament with Modge Podge or another clear-drying glue and use a funnel to pour the glass glitter into the ornaments. Cover the opening of the ornament and shake it until the inside surface of the ornament is thoroughly covered. As the glue dries over the next several hours it will become transparent and your ornament should start to resemble the ones in the above photo.